Makefile environment variable changes between recipes

Makefile environment variable changes between recipes

I'm attempting to create a single log file that tracks and reports the
results of each recipe as the make process moves through the makefile.
To do this, I'm creating an environment variable to hold my logfile
reference like so:
LOGDIR = logs
LOGFILE = $(LOGDIR)/$(shell date --iso=seconds).log
The intention is then to add relevant messaging to the log file by using
echo "message" >> $(LOGFILE)
Trouble is, when processing moves from one recipe to the next, the
environment variable is re-evaluated, resulting in a new log file from
every recipe in my makefile.
Why does the environment variable get re-evaluated, and how can I prevent
this to use a single global reference to a logfile?
I thought that using the $(shell operator) syntax prevents re-evaluation
of the variable, based on Aaron's answer here.